Was no sure what to do here. Flop seems dry, only reasonable draw could be OESD with 67, still I think when betting out myself in most cases only an A or better will continue so I decided to check behind and call turn if needed. What do you think of my play?

KK with A on board is quite difficult. I check here about 50% of times. This is better against aggressive opponents who bet themselves if you show weakness on flop. In this way you can extract at least one bet from weaker PPs or one bluff.
Although you have onlu 11 hands on your opponents, they seem fishy. How they played their hands so far ?
To conclude this - I like your line here. Dont think that they would fold Ax or better on river, you could be also ahead here but not often enough to make bet profitable.

I think c-bet on that board is better than checking, since I would c-bet there with AK/KQ/JJ and every other hand that I raised pf, so I don´t see any reason why not to bet with KK.
turn and river are fine